{
  "annotation_id": "0f9a2438-3a4c-4ec7-b185-67b250f6eb26",
  "date_created": "2026-03-02T18:01:49.338000Z",
  "date_modified": "2026-03-02T18:01:49.338000Z",
  "file_hash": "38f40c72e6e6398e2b8ba979e4dce70b05adab218590eb86736481a41f62f261",
  "private": false,
  "record": {
    "abstract": "For finite-dimensional bipartite quantum systems, we find the exact size of\nthe largest balls, in spectral $l_p$ norms for $1 \\le p \\le \\infty$, of\nseparable (unentangled) matrices around the identity matrix. This implies a\nsimple and intutively meaningful geometrical sufficient condition for\nseparability of bipartite density matrices: that their purity $\\tr \\rho^2$ not\nbe too large. Theoretical and experimental applications of these results\ninclude algorithmic problems such as computing whether or not a state is\nentangled, and practical ones such as obtaining information about the existence\nor nature of entanglement in states reached by NMR quantum computation\nimplementations or other experimental situations.",
    "arxiv_id": "quant-ph/0204159",
    "authors": [
      "Leonid Gurvits",
      "Howard Barnum"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.062311",
    "journal_ref": "Physical Review A, Vol. 66, Article no. 062311 (Dec. 2002)",
    "title": "Largest separable balls around the maximally mixed bipartite quantum   state",
    "url": "https://arxiv.org/abs/quant-ph/0204159"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "321b172c-9ac8-4440-bc06-e015c4f895ff",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}